Questions: Solve for (x) (z=2x-3y)

Solution Steps

To solve for $x$ in the equation $z = 2x - 3y$, we need to isolate $x$ on one side of the equation. This involves rearranging the equation by performing algebraic operations.

1. Add $3y$ to both sides of the equation to move the $y$-term to the left side.
2. Divide both sides by 2 to solve for $x$.

Starting with the equation: $$z = 2x - 3y$$ we add $3y$ to both sides to isolate the term with $x$: $$z + 3y = 2x$$

Next, we divide both sides of the equation by 2 to solve for $x$: $$x = \frac{z + 3y}{2}$$

Given $z = 10$ and $y = 2$, we substitute these values into the equation: $$x = \frac{10 + 3 \cdot 2}{2}$$

Simplify the expression to find the value of $x$: $$x = \frac{10 + 6}{2} = \frac{16}{2} = 8.0$$

Final Answer